Chapter 100 17.2 Generating groups of primitives for images

There is more than one way to form an open genome. In 1990, Carl Sims used the supercomputing power of the second-generation Connector (CM2) to design a new artificial world composed of variable-length genes, which is more advanced than the plant image world he designed.Sims' neat trick is to create a genome made up of small equations rather than long strings of numbers.Each fixed-length gene in his original gene pool controlled a visual parameter of the plant; this new gene pool has equations of variable length and freely expandable to draw various curves, colors and shapes. Sims' equations -- or genes -- are small self-contained logic units in a computer language (LISP).Each module is an arithmetic instruction, such as add, subtract, multiply, cosine, sine.Sims refers to these units collectively as "primitives"—they form a logical alphabet.With an appropriate logical alphabet at hand, any equation can be constructed, just as any phonetic sentence can be synthesized with an appropriately diverse list of phonetic elements.Addition, multiplication, cosine, etc. can be combined to produce any mathematical equation we can think of.Since any shape can be represented by an equation, this primitive alphabet can also draw any kind of image.Increasing the complexity of the equations magically increases the complexity of the resulting image.

The equation gene pool also has an unexpected benefit.In the original Sims world (and in Tom Ray's Earth and Danny Hillis's co-evolved parasite world), organisms are strings of digits that randomly switch one number at a time, like Like the books in the Borges library, changing one letter at a time.In Sims' modified world, however, organisms become strings of logical primitives that randomly switch one primitive at a time.Still using the example of the Borges Library, this time the words are swapped instead of the letters.Every word in every book is spelled correctly, making every page of every book more meaningful.However, for the Borges library, which uses words as raw materials, at least tens of thousands of words are needed to make this soup, Sims can list all possible combinations with only a dozen or so mathematical primitives. the equation.

The fundamental advantage of evolving logic units rather than digital bits is that it can immediately lead the system on the road to the open universe.The logic unit itself is the function, not just the value of the function like the digital bit.Adding or exchanging a logical primitive anywhere, the overall function of the program will be transformed or expanded, so that new functions and new things will emerge in the system. And that's what Sims found.His equations evolve entirely new images and display them on a computer screen.This new space is so rich it blows Sims away.Since primitives consist only of logical components, Sims' LISP alphabet ensures that most equations draw pictures of some sort.Instead of flooding the screen with blurry, gray images, Sims will be able to see stunning scenery wherever they “wander”. "Art" seems to have become something that comes at your fingertips.In the beginning, the screen is filled with wild red and blue zigzag lines.The next moment, the upper part of the screen was dotted with yellow spots.After that, a hazy horizontal line appears under the spots, and then, there are waves of heavy ink and ink accompanied by a blue line of sea and sky.Then, the spots faded into bright yellow halos like buttercups.Almost every round of the picture shows amazing creativity.Within an hour, a thousand magnificent images are evoked from their hiding places and unfolded before us for the first and last time.It's like standing behind the world's greatest painter and watching him create sketches that never repeat a theme or style.

When Sims take a picture, multiply its variants, and pick another from it, he's evolving more than just the image.Appearances aside, Sims evolve logic.A relatively small logic equation can paint a dizzyingly complex picture.Sims' system once evolved the following logic code: (cos (round (atan (log (invert y) (+ (bump (+ (round xy) y) #(0.46 0.82 0.65) 0.02 #(0.1 0.06 0.1) #(0.99 0.06 0.41) 1.47 8.7 3.7) (color- grad (round (+ yy) (log (invert x) (+ (invert y) (round (+ yx) (bump (warped-ifs (round yy) y 0.08 0.06 7.4 1.65 6.1 0.54 3.1 0.26 0.73 15.8 5.7 8.9 0.49 7.2 15.6 0.98) #(0.46 0.82 0.65) 0.02 #(0.1 0.06 0.1) #(0.99 0.06 0.41) 0.83 8.7 2.6))))) 3.1 6.8 #(0.95 0.7 0.59) 0.57))) #(0.10 37))) #(0.10 37)) (vector y 0.09 (cos (round yy)))))

The equation paints a striking picture on Sims' color screen: the afterglow of the setting sun at the North Pole reflected on two icicles, crystal clear; the distant horizon is pale and serene.This is comparable to the masterpiece of an amateur painter.Sims told me: "The evolution of this equation from start to finish took only a few minutes—a lot more work than that, if humans did it on purpose." But Sims can't explain the logic behind the equation and why it draws a picture of ice.Sims are as ignorant of this equation as we are.The logic hidden in the equation can no longer be deciphered by simple and clear mathematics.